Proofs of theorems for the JRSS-B paper `Likelihood ratio tests in linear mixed models with one variance component'

Proofs of theorems for the JRSS-B paper `Likelihood ratio tests in linear mixed models with one variance component

Functional regression via variational bayes

We introduce variational Bayes methods for fast approximate inference in functional regression analysis. Both the standard cross-sectional and the increasingly common longitudinal settings are treated. The method- ology allows Bayesian functional regression analyses to be conducted with- out the computational overhead of Monte Carlo methods. Confidence in- tervals of the model parameters are obtained both using the approximate variational approach and nonparametric resampling of clusters. The latter approach is possible because our variational Bayes functional regression ap- proach is computationally efficient. A simulation study indicates that varia- tional Bayes is highly accurate in estimating the parameters of interest and in approximating the Markov chain Monte Carlo-sampled joint posterior distribution of the model parameters. The methods apply generally, but are motivated by a longitudinal neuroimaging study of multiple sclerosis patients. Code used in simulations is made available as a web-supplement

Semiparametric Regression in Capture-Recapture Modelling

Capture-recapture models were developed to estimate survival using data arising from marking and monitoring wild animals over time. Variation in the survival process may be explained by incorporating relevant covariates. We develop nonparametric and semiparametric regression models for estimating survival in capture-recapture models. A fully Bayesian approach using MCMC simulations was employed to estimate the model parameters. The work is illustrated by a study of Snow petrels, in which survival probabilities are expressed as nonlinear functions of a climate covariate, using data from a 40-year study on marked individuals, nesting at Petrels Island, Terre Adelie

AN OVERVIEW OF OBSERVATIONAL SLEEP RESEARCH WITH APPLICATION TO SLEEP STAGE TRANSITIONING

In this manuscript we give an overview of observational sleep research with a particular emphasis on sleep stage transitions. Sleep states represent a categorization of sleep electroencephalogram behavior over the night. We postulate that the rate of transitioning between sleep states is an important predictor of health. This claim is evaluated by comparing subjects with sleep disordered breathing to matched controls

Modelling subject-specific childhood growth using linear mixed-effect models with cubic regression splines.

Childhood growth is a cornerstone of pediatric research. Statistical models need to consider individual trajectories to adequately describe growth outcomes. Specifically, well-defined longitudinal models are essential to characterize both population and subject-specific growth. Linear mixed-effect models with cubic regression splines can account for the nonlinearity of growth curves and provide reasonable estimators of population and subject-specific growth, velocity and acceleration.We provide a stepwise approach that builds from simple to complex models, and account for the intrinsic complexity of the data. We start with standard cubic splines regression models and build up to a model that includes subject-specific random intercepts and slopes and residual autocorrelation. We then compared cubic regression splines vis-à-vis linear piecewise splines, and with varying number of knots and positions. Statistical code is provided to ensure reproducibility and improve dissemination of methods. Models are applied to longitudinal height measurements in a cohort of 215 Peruvian children followed from birth until their fourth year of life.Unexplained variability, as measured by the variance of the regression model, was reduced from 7.34 when using ordinary least squares to 0.81 (p < 0.001) when using a linear mixed-effect models with random slopes and a first order continuous autoregressive error term. There was substantial heterogeneity in both the intercept (p < 0.001) and slopes (p < 0.001) of the individual growth trajectories. We also identified important serial correlation within the structure of the data (ρ = 0.66; 95 % CI 0.64 to 0.68; p < 0.001), which we modeled with a first order continuous autoregressive error term as evidenced by the variogram of the residuals and by a lack of association among residuals. The final model provides a parametric linear regression equation for both estimation and prediction of population- and individual-level growth in height. We show that cubic regression splines are superior to linear regression splines for the case of a small number of knots in both estimation and prediction with the full linear mixed effect model (AIC 19,352 vs. 19,598, respectively). While the regression parameters are more complex to interpret in the former, we argue that inference for any problem depends more on the estimated curve or differences in curves rather than the coefficients. Moreover, use of cubic regression splines provides biological meaningful growth velocity and acceleration curves despite increased complexity in coefficient interpretation.Through this stepwise approach, we provide a set of tools to model longitudinal childhood data for non-statisticians using linear mixed-effect models

A Research Agenda for Helminth Diseases of Humans: Modelling for Control and Elimination

Mathematical modelling of helminth infections has the potential to inform policy and guide research for the control and elimination of human helminthiases. However, this potential, unlike in other parasitic and infectious diseases, has yet to be realised. To place contemporary efforts in a historical context, a summary of the development of mathematical models for helminthiases is presented. These efforts are discussed according to the role that models can play in furthering our understanding of parasite population biology and transmission dynamics, and the effect on such dynamics of control interventions, as well as in enabling estimation of directly unobservable parameters, exploration of transmission breakpoints, and investigation of evolutionary outcomes of control. The Disease Reference Group on Helminth Infections (DRG4), established in 2009 by the Special Programme for Research and Training in Tropical Diseases (TDR), was given the mandate to review helminthiases research and identify research priorities and gaps. A research and development agenda for helminthiasis modelling is proposed based on identified gaps that need to be addressed for models to become useful decision tools that can support research and control operations effectively. This agenda includes the use of models to estimate the impact of large-scale interventions on infection incidence; the design of sampling protocols for the monitoring and evaluation of integrated control programmes; the modelling of co-infections; the investigation of the dynamical relationship between infection and morbidity indicators; the improvement of analytical methods for the quantification of anthelmintic efficacy and resistance; the determination of programme endpoints; the linking of dynamical helminth models with helminth geostatistical mapping; and the investigation of the impact of climate change on human helminthiases. It is concluded that modelling should be embedded in helminth research, and in the planning, evaluation, and surveillance of interventions from the outset. Modellers should be essential members of interdisciplinary teams, propitiating a continuous dialogue with end users and stakeholders to reflect public health needs in the terrain, discuss the scope and limitations of models, and update biological assumptions and model outputs regularly. It is highlighted that to reach these goals, a collaborative framework must be developed for the collation, annotation, and sharing of databases from large-scale anthelmintic control programmes, and that helminth modellers should join efforts to tackle key questions in helminth epidemiology and control through the sharing of such databases, and by using diverse, yet complementary, modelling approaches

A Research Agenda for Helminth Diseases of Humans: Diagnostics for Control and Elimination Programmes

Diagnostic tools appropriate for undertaking interventions to control helminth infections are key to their success. Many diagnostic tests for helminth infection have unsatisfactory performance characteristics and are not well suited for use in the parasite control programmes that are being increasingly implemented. Although the application of modern laboratory research techniques to improve diagnostics for helminth infection has resulted in some technical advances, uptake has not been uniform. Frequently, pilot or proof of concept studies of promising diagnostic technologies have not been followed by much needed product development, and in many settings diagnosis continues to rely on insensitive and unsatisfactory parasitological or serodiagnostic techniques. In contrast, PCR-based xenomonitoring of arthropod vectors, and use of parasite recombinant proteins as reagents for serodiagnostic tests, have resulted in critical advances in the control of specific helminth parasites. The Disease Reference Group on Helminths Infections (DRG4), established in 2009 by the Special Programme for Research and Training in Tropical Diseases (TDR) was given the mandate to review helminthiases research and identify research priorities and gaps. In this review, the diagnostic technologies relevant to control of helminth infections, either available or in development, are reviewed. Critical gaps are identified and opportunities to improve needed technologies are discussed